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Existence, compactness and non-compactness results on the fractional Yamabe problem

Banff International Research Station for Mathematical Innovation and Discovery

Let $(X^{n+1}, g^+)$ be an $(n+1)$-dimensional asymptotically hyperbolic manifold with a conformal infinity $(M^n, [h])$. The fractional Yamabe problem consists in finding a metric in the conformal class $[h]$ whose fractional scalar curvature is constant. In this talk, I will present some recent results concerning existence of solutions to the fractional Yamabe problem, and also properties of compactness and non compactness of its solution set, in comparison with what is known in the classical case. These results are in collaboration with Seunghyeok Kim and Juncheng Wei.

Mathematics; Partial differential equations; Differential geometry

video/mp4

Author affiliation: Pontificia Universidad Catòlica de Chile

2017-11-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63668

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/